i understand that i posted questions like crazy but you have to understand i do try them out i use this website as a last resort and mainly to see what you think i should do. there are still a few i can't get.
An object whose height is 3.5 cm is at a distance of 8.5 cm from a spherical concave mirror. Its image is real and has a height of 11.2 cm. Calculate the radius of curvature of the mirror. i got this one the answer is .130 m
but the second part asks for the new Do and i have tried everything and i can't seem to get it with having the two unknowns.
also the one that asks for time...A laser beam enters a 12.5 cm thick glass window at an angle of 39° (from the normal). The index of refraction of the glass is 1.46. the angle from which the beam crosses through the glass is 25.5 deg from the normal. How long does it take the beam to pass through the plate?
i know you have to draw a diagram and what not but i just don't understand how you use the trig functions.
the only other one i can't get is the shadow one that goes as fallows...2.0- m-long vertical stick in air casts a shadow 1.8 m long. If the same stick is placed at 08:00hrs in air in a flat bottomed pool of salt water half the height of the stick, how long is the shadow on the floor of the pool? (For this pool, n = 1.56.)
<<.A laser beam enters a 12.5 cm thick glass window at an angle of 39° (from the normal). The index of refraction of the glass is 1.46. the angle from which the beam crosses through the glass is 25.5 deg from the normal. How long does it take the beam to pass through the plate? >>
The speed of light through the glass is V = c/N = (3.00*10^10 cm/s)/1.46
= 2.05*10^10 cm/s
The distance the light travels thropugh the glass is
D = 12.5/cos 25.5 = 13.85 cm
Time = D/V
I answered a problem about the length of a shadow a stick on a saltwater pool bottom previously. Look again.
Please make sure you DO NOT use a tutor's name in place of your own. It's a form of impersonation, and you can cause yourself problems by doing this.
Thanks.
You cannot find new Do unless position of new image or height of new image is given.
With regard to the length of the shadow at the bottom of a pool, I was calculating the distance of the end of the shadow from a point directly below the stick. The bottom end of the shadow is displaced the same as it is at the surface. The length of the shadow at the bottom of the pool is the same as it is at the surface: 1.8 m. This is because the rays that pass by the bottom and the top of the pool remain parallel.
No worries, I'm here to help! Let's go through each question step by step and work on finding the answers together.
1. Calculating the radius of curvature of the mirror:
To solve this problem, we can use the mirror formula:
1/f = 1/do + 1/di,
where f represents the focal length, do is the object distance, and di is the image distance.
Given:
Height of the object (ho) = 3.5 cm
Height of the image (hi) = 11.2 cm
Object distance (do) = 8.5 cm
We need to find the radius of curvature (R). We can start by finding the image distance (di) using the magnification formula. For concave mirrors, the magnification (M) is given by:
M = -hi/ho = di/do
Substituting the given values, we have:
-11.2 cm / 3.5 cm = di / 8.5 cm
Solving for di, we find:
di = -27.4 cm
Now we can use the mirror formula to find the radius of curvature:
1/f = 1/do + 1/di
Substituting the known values:
1/R = 1/8.5 cm + 1/-27.4 cm
Simplifying the equation and solving for R, we get:
R = 0.13 m
For the second part of this question, you mentioned the "new Do." Could you please provide more context or clarify what you mean by "new Do"?
2. Calculating the time it takes for the laser beam to pass through the glass:
To solve this problem, we can use Snell's Law, which relates the angles of incidence and refraction to the indices of refraction:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
Given:
Thickness of the glass plate (d) = 12.5 cm
Index of refraction of the glass (n2) = 1.46
Angle of incidence (angle1) = 39 degrees
Angle of refraction (angle2) = 25.5 degrees
We need to find the time it takes for the beam to pass through the glass plate.
First, convert the angles to radians by multiplying them by pi/180:
angle1 = 39 * (pi/180) radians
angle2 = 25.5 * (pi/180) radians
Next, use Snell's Law to find the index of refraction of the medium the beam is coming from (n1):
n1 = n2 * (sin(angle2) / sin(angle1))
Substituting the given values:
n1 = 1.46 * (sin(angle2) / sin(angle1))
Now, we can calculate the time it takes for the beam to pass through the plate using the formula:
time = d / (c * n1),
where c is the speed of light (approximately 3 * 10^8 m/s).
Substituting the known values and converting units:
time = (12.5 cm) / (3 * 10^8 m/s * n1)
Solving for time, we find the answer.
3. Finding the length of the shadow in the pool:
To solve this problem, we can use the concept of similar triangles. The ratio of the lengths of corresponding sides of similar triangles is equal to the ratio of the lengths of the other sides.
Given:
Length of the stick (L) = 2.0 m
Length of the shadow in air (S) = 1.8 m
Index of refraction of the saltwater (n) = 1.56
To find the length of the shadow in the pool (spool), we can set up the following proportion:
(L - S) / L = spool / S
Solving for spool, we get:
spool = S * (L - S) / L
Substituting the given values and solving, we can find the length of the shadow in the pool.
I hope this explanation helps! If you have any further questions or need additional clarification, please let me know.